scholarly journals A note on the parabolic identification problem with involution and Dirichlet condition

2020 ◽  
Vol 99 (3) ◽  
pp. 130-139
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
A. Sarsenbi ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Difference Scheme ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
The Difference

A space source of identification problem for parabolic equation with involution and Dirichlet condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem is presented. Furthermore, stability estimates for the difference scheme of the source identification parabolic problem are presented. Numerical results are given.

scholarly journals Parabolic time dependent source identification problem with involution and Neumann condition

2021 ◽  
Vol 102 (2) ◽  
pp. 5-15
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Parabolic Equation ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Time Dependent ◽  
Neumann Condition ◽  
Stability Estimates ◽  
Well Posedness

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given.

Source identification problems for hyperbolic differential and difference equations

2019 ◽  
Vol 27 (3) ◽  
pp. 301-315 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fathi Emharab
Keyword(s):  
Difference Scheme ◽  
Source Identification ◽  
Identification Problem ◽  
Stability Estimates ◽  
Identification Problems ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
First Order ◽  
Accuracy Difference ◽  
The Difference

Abstract In the present study, a source identification problem for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the source identification problem are established. Furthermore, a first-order-of-accuracy difference scheme for the numerical solution of the source identification problem is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example, and some numerical results are presented.

scholarly journals A note on well-posedness of source identification elliptic problem in a Banach space

2020 ◽  
Vol 99 (3) ◽  
pp. 96-104
Author(s):  
A. Ashyralyev ◽  
◽  
C. Ashyralyyev ◽  
V.G. Zvyagin ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Elliptic Problem ◽  
Source Identification ◽  
Elliptic Equations ◽  
Identification Problem ◽  
Stability Estimates ◽  
Well Posedness ◽  
Identification Problems ◽  
Coercive Stability

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in H¨older norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained.

scholarly journals On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem

2021 ◽  
Vol 102 (2) ◽  
pp. 45-53
Author(s):  
C. Ashyralyyev ◽  
◽  
G. Akyuz ◽  
◽  
Keyword(s):  
Approximate Solution ◽  
Difference Scheme ◽  
Fourth Order ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Uniqueness Of The Solution ◽  
Accuracy Difference ◽  
The Difference ◽  
Overdetermined Boundary Value Problem ◽  
Coercive Stability

In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi-point overdetermined boundary value problem for multidimensional elliptic partial differential equations.

scholarly journals A Note on the Stability of the Integral-Differential Equation of the Parabolic Type in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Difference Scheme ◽  
Unique Solvability ◽  
Parabolic Type ◽  
Stability Estimates ◽  
The Difference ◽  
The Stability ◽  
Integral Differential Equation

The integral-differential equation of the parabolic type in a Banach space is considered. The unique solvability of this equation is established. The stability estimates for the solution of this equation are obtained. The difference scheme approximately solving this equation is presented. The stability estimates for the solution of this difference scheme are obtained.

scholarly journals A note on the hyperbolic-parabolic identification problem with involution and Dirichlet boundary condition

2020 ◽  
Vol 99 (3) ◽  
pp. 120-129
Author(s):  
Maksat Ashyraliyev ◽  
◽  
Maral A. Ashyralyyeva ◽  
Allaberen Ashyralyev ◽  
◽  
...  
Keyword(s):  
Source Identification ◽  
Test Problem ◽  
Dirichlet Boundary ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Simple Test ◽  
Order Of Accuracy ◽  
First Order ◽  
The Stability

In the present paper, a source identification problem for hyperbolic-parabolic equation with involution and Dirichlet condition is studied. The stability estimates for the solution of the source identification hyperbolicparabolic problem are established. The first order of accuracy stable difference scheme is constructed for the approximate solution of the problem under consideration. Numerical results are given for a simple test problem.

scholarly journals On the Crank-Nicolson difference scheme for the time-dependent source identification problem

2021 ◽  
Vol 102 (2) ◽  
pp. 35-44
Author(s):  
A. Ashyralyev ◽  
◽  
M. Urun ◽  
◽  
◽  
...  
Keyword(s):  
Difference Scheme ◽  
Source Identification ◽  
Identification Problem ◽  
Stability Estimates ◽  
Differential Problem ◽  
Order Of Accuracy ◽  
Local Boundary ◽  
Non Local ◽  
The One ◽  
Crank Nicolson

In this study the source identification problem for the one-dimensional Schr¨odinger equation with non-local boundary conditions is considered. A second order of accuracy Crank-Nicolson difference scheme for the numerical solution of the differential problem is presented. Stability estimates are proved for the solution of this difference scheme. Numerical results are given.

scholarly journals On stability of the third order partial delay differential equation with involution and Dirichlet condition

2021 ◽  
Vol 102 (2) ◽  
pp. 25-34
Author(s):  
A. Ashyralyev ◽  
◽  
S. Ibrahim ◽  
E. Hincal ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Difference Scheme ◽  
Delay Differential Equation ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Third Order ◽  
Differential Problem ◽  
The Third ◽  
Partial Delay ◽  
Delay Differential

In this paper the stability of the initial value problem for the third order partial delay differential equation with involution is investigated. The first order of accuracy absolute stable difference scheme for the solution of the differential problem is presented. Stability estimates for the solution of this difference scheme are proved. Numerical results are provided.

Well-posedness of a nonlocal boundary value difference elliptic problem

2019 ◽  
Vol 14 (5) ◽  
pp. 507
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Well Posedness ◽  
The Difference ◽  
The Stability ◽  
Coercive Stability ◽  
Second Order Of Approximation

The second order of approximation two-step difference scheme for the numerical solution of a nonlocal boundary value problem for the elliptic differential equation [see formula in PDF] in an arbitrary Banach space E with the positive operator A is presented. The well-posedness of the difference scheme in Banach spaces is established. In applications, the stability, almost coercive stability and coercive stability estimates in maximum norm in one variable for the solutions of difference schemes for numerical solution of two type elliptic problems are obtained.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

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